Problem Statement

You are given an integer sequence A=(A_1,A_2,\dots,A_N) of length N.

Find the maximum value of \displaystyle \sum_{i=1}^{M} i \times B_i for a contiguous subarray B=(B_1,B_2,\dots,B_M) of A of length M.

Notes

A contiguous subarray of a number sequence is a sequence that is obtained by removing 0 or more initial terms and 0 or more final terms from the original number sequence.

For example, (2, 3) and (1, 2, 3) are contiguous subarrays of (1, 2, 3, 4), but (1, 3) and (3,2,1) are not contiguous subarrays of (1, 2, 3, 4).

Constraints

• 1 \le M \le N \le 2 \times 10^5
• - 2 \times 10^5 \le A_i \le 2 \times 10^5
• All values in input are integers.

Sample Input 1

4 2
5 4 -1 8

Sample Output 1

15

When B=(A_3,A_4), we have \displaystyle \sum_{i=1}^{M} i \times B_i = 1 \times (-1) + 2 \times 8 = 15. Since it is impossible to achieve 16 or a larger value, the solution is 15.

Note that you are not allowed to choose, for instance, B=(A_1,A_4).

Sample Input 2

10 4
-3 1 -4 1 -5 9 -2 6 -5 3

Sample Output 2

31

Problem Statement

You are given a sequence A=(A_1,A_2,\dots,A_{3N}) of length 3N where each of 1,2,\dots, and N occurs exactly three times.

For i=1,2,\dots,N, let f(i) be the index of the middle occurrence of i in A. Sort 1,2,\dots,N in ascending order of f(i).

Formally, f(i) is defined as follows.

• Suppose that those j such that A_j = i are j=\alpha,\beta,\gamma\ (\alpha < \beta < \gamma). Then, f(i) = \beta.

Constraints

• 1\leq N \leq 10^5
• 1 \leq A_j \leq N
• i occurs in A exactly three times, for each i=1,2,\dots,N.
• All input values are integers.

Sample Input 1

3
1 1 3 2 3 2 2 3 1

Sample Output 1

1 3 2

• 1 occurs in A at A_1,A_2,A_9, so f(1) = 2.
• 2 occurs in A at A_4,A_6,A_7, so f(2) = 6.
• 3 occurs in A at A_3,A_5,A_8, so f(3) = 5.

Thus, f(1) < f(3) < f(2), so 1,3, and 2 should be printed in this order.

Sample Input 2

1
1 1 1

Sample Output 2

1

Sample Input 3

4
2 3 4 3 4 1 3 1 1 4 2 2

Sample Output 3

3 4 1 2

Problem Statement

A sequence of n numbers, S = (s_1, s_2, \dots, s_n), is said to be non-decreasing if and only if s_i \leq s_{i+1} holds for every i (1 \leq i \leq n - 1).

Given are non-decreasing sequences of N integers each: A = (a_1, a_2, \dots, a_N) and B = (b_1, b_2, \dots, b_N).
Consider a non-decreasing sequence of N integers, C = (c_1, c_2, \dots, c_N), that satisfies the following condition:

• a_i \leq c_i \leq b_i for every i (1 \leq i \leq N).

Find the number, modulo 998244353, of sequences that can be C.

Constraints

• 1 \leq N \leq 3000
• 0 \leq a_i \leq b_i \leq 3000 (1 \leq i \leq N)
• The sequences A and B are non-decreasing.
• All values in input are integers.

Sample Input 1

2
1 1
2 3

Sample Output 1

5

There are five sequences that can be C, as follows.

• (1, 1)
• (1, 2)
• (1, 3)
• (2, 2)
• (2, 3)

Note that (2, 1) does not satisfy the condition since it is not non-decreasing.

Sample Input 2

3
2 2 2
2 2 2

Sample Output 2

1

There is one sequence that can be C, as follows.

• (2, 2, 2)

Sample Input 3

10
1 2 3 4 5 6 7 8 9 10
1 4 9 16 25 36 49 64 81 100

Sample Output 3

978222082

Be sure to find the count modulo 998244353.

Problem Statement

We have an integer sequence A and a notebook. The notebook has 10^9 pages.

You are given Q queries. Each query is of one of the following four kinds:

ADD x: append an integer x to the tail of A.

DELETE: remove the last term of A if A is not empty; do nothing otherwise.

SAVE y: erase the sequence recorded on the y-th page of the notebook, and record the current A onto the y-th page.

LOAD z: replace A with the sequence recorded on the z-th page of the notebook.

Initially, A is an empty sequence, and an empty sequence is recorded on each page of the notebook. Process Q queries successively in the given order and print the last term of A after processing each query.

The use of fast input and output methods is recommended because of potentially large input and output.

Constraints

• 1 \leq Q \leq 5 \times 10^5
• 1 \leq x, y, z \leq 10^9
• Q, x, y, and z are integers.
• Each of the given queries is of one of the four kinds in the Problem Statement.

Sample Input 1

11
ADD 3
SAVE 1
ADD 4
SAVE 2
LOAD 1
DELETE
DELETE
LOAD 2
SAVE 1
LOAD 3
LOAD 1

Sample Output 1

3 3 4 4 3 -1 -1 4 4 -1 4

Initially, A is an empty sequence, so A = (), and an empty sequence is recorded on each page of the notebook.

• By the 1-st query, 3 is appended to the tail of A, resulting in A = (3).
• By the 2-nd query, the sequence recorded on the 1-st page of the notebook becomes (3). It remains that A = (3).
• By the 3-rd query, 4 is appended to the tail of A, resulting in A = (3, 4).
• By the 4-th query, the sequence recorded on the 2-nd page of the notebook becomes (3, 4). It remains that A = (3, 4).
• By the 5-th query, A is replaced by (3), which is recorded on the 1-st page of the notebook, resulting in A = (3).
• By the 6-th query, the last term of A is removed, resulting in A = ().
• By the 7-th query, nothing happens because A is already empty. It remains that A = ().
• By the 8-th query, A is replaced by (3,4), which is recorded on the 2-nd page of the notebook, resulting in A = (3, 4).
• By the 9-th query, the sequence recorded on the 1-st page of the notebook becomes (3, 4). It remains that A = (3, 4).
• By the 10-th query, A is replaced by (), which is recorded on the 3-rd page of the notebook, resulting in A = ().
• By the 11-th query, A is replaced by (3, 4), which is recorded on the 1-st page of the notebook, resulting in A = (3, 4).

Sample Input 2

21
ADD 4
ADD 3
DELETE
ADD 10
LOAD 7
SAVE 5
SAVE 5
ADD 4
ADD 4
ADD 5
SAVE 5
ADD 2
DELETE
ADD 1
SAVE 5
ADD 7
ADD 8
DELETE
ADD 4
DELETE
LOAD 5

Sample Output 2

4 3 4 10 -1 -1 -1 4 4 5 5 2 5 1 1 7 8 7 4 7 1

Problem Statement

There are N boxes. The i-th box has a shape of a rectangular cuboid whose height, width, and depth are h_i,w_i, and d_i, respectively.

Determine if there are two boxes such that one's height, width, and depth are strictly greater than those of the other after rotating them if necessary.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq h_i,w_i,d_i \leq 10^9
• All input values are integers.

Sample Input 1

3
19 8 22
10 24 12
15 25 11

Sample Output 1

Yes

If you rotate the 2-nd box to swap its height and depth, the 3-rd box will have greater height, depth, and width.

Sample Input 2

3
19 8 22
10 25 12
15 24 11

Sample Output 2

No

Sample Input 3

2
1 1 2
1 2 2

Sample Output 3

No